The invention relates to a suction braking apparatus for the braking and overlapping of sheets to be stacked, particularly sheets of paper, which comprises a suction chamber provided with suction holes, a cover plate perforated in register therewith, and at least one perforated control belt movable between cover plate and suction chamber at right angles to the direction of travel of the sheets. A suction braking apparatus of this type has become part of the prior art through German Pat. No. 1,917,616 and German patent of addition No. 2,000,078.